Videos, examples, solutions to help Grade 8 students know the conditions for which a linear equation will have a unique solution, no solution, or infinitely many solutions.
Plans and Worksheets for Grade 8
Plans and Worksheets for all Grades
Lessons for Grade 8
Common Core For Grade 8
New York State Common Core Math Grade 8, Module 4, Lesson 7
Lesson 7 Outcome
• Students know the conditions for which a linear equation will have a unique solution, no solution, or infinitely
Lesson 7 Summary
• There are three classifications of solutions to linear equations: one solution (unique solution), no solution, or
infinitely many solutions.
Equations with no solution will, after being simplified, have coefficients of x that are the same on both sides of the
equal sign and constants that are different. For example, x + b = x + c, where b, c are constants that are not
equal. A numeric example is 8x + 5 = 8x - 3.
Equations with infinitely many solutions will, after being simplified, have coefficients of x and constants that are
the same on both sides of the equal sign. For example, x + a = x + a, where a is a constant. A numeric example is
6x + 1 = 1 + 6x.
NYS Math Module 4 Grade 8 Lesson 7 Classwork
Solve each of the following equations for x.
1. 7x - 3 = 5x + 5
2. 7x - 3 = 7x + 5
3. 7x - 3 = -3 + 7x
Note: if the coefficients of x are different and the value of the constants are the same, the only solution
is x = 0. For example, 2x + 12 = x + 12
Activity: What can
we see in an equation that will tell us about the solution to the equation?
Give a brief explanation as to what kind of solution(s) you expect the following linear equations to have. Transform the
equation into a simpler form if necessary.
4. 11x - 2x + 15 = 8 + 7 + 9x
5. 3(x -14) + 1 = -4x + 5
6. -3x + 32 - 7x = -2(5x + 10)
7. 1/2(8x + 26) = 13 + 4x
8. Write two equations that have no solutions.
9. Write two equations that have one unique solution each.
10. Write two equations that have infinitely many solutions.
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